Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)

On 1/8/25 5:06 PM, WM wrote:

The set {1, 2, 3, ...} is smaller by one element than the set {0, 1, 2, 3, ...}. Proof: {0, 1, 2, 3, ...} \ {1, 2, 3, ...} = {0}. Cardinality cannot describe this difference because it covers only mappings of elements which have almost all elements as successors.
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But Alelph_0, the size of the second, is also the size of the first, as Aleph_0 - 1 is Aleph_0.